Axion Dark Matter : Motivation and Search Techniques

Pierre Sikivie

UCLA DM Conference February 17, 2016

•  Motivation

Axions solve the strong CP problem

Axions are present in many models of beyond-the-Standard Model physics Axions are a form of cold dark matter Axion BEC explains the existence and properties of caustic rings in galactic halos

•  Axion Search Techniques

the cavity haloscope the axion helioscope

shining light through walls NMR methods axion mediated long-range forces

LC circuit atomic transitions

The Strong CP Problem 2

QCD 2... 32a agL G G µνµνθ π

= +

%

where arg ( ... )u tdm m mθ θ = − arg det ( )u dY Yθ= −

The absence of P and CP violation in the strong interactions requires

from upper limit on the neutron electric dipole moment

1010θ −≤

If a symmetry is assumed,

relaxes to zero,

PQU (1)

2

2

1... .32 2

a a

a

a gL G G a af

µν µµν µπ

= + + ∂ ∂ + ..

%

and a light neutral pseudoscalar particle is predicted: the axion.

Weinberg, Wilczek 1978

�̄ =a

fa

f f

a

a

γγ

610 GeVeVa

a fm 6 ;

= 0.97 in KSVZ model 0.36 in DFSZ model

gγ

Laf̄f = igfa

faf̄�5f

La�� = g�a

fa�E · �B

The remaining axion window

laboratory searches

510 15101010 (GeV)af

(eV)am 1 510− 1010−

stellar evolution

cosmology

Axion production by vacuum realignment

2 2 21 1 1 1

1

1

2

1

2( ) ( ) ( ) ( )a a at t t tt

n m a f α ; ;

GeVT ≥ 1 GeVT ≤ 1

V

a

V

a

1

0

3 76

0 1( ) ( )a aa aR

Rt tm mnρ −⎛ ⎞ ∝ ⎜ ⎟

⎝ ⎠ ;

initial misalignment angle

J. Preskill, M. Wise & F. Wilczek, L. Abbott & PS, M. Dine & W. Fischler, 1983

Cold axion properties

•  number density

•  velocity dispersion •  phase space density

5 347 31

3 12

( )4 10( )cm 10 GeV ( )

af a tn ta t

⎛ ⎞⋅ ⎛ ⎞ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠:

1

1

( )1( )

v( )a

a tm t a t

tδ

:

83 361

1234

3

(2 )( ) 1010 GeV( v)

a

a

fn tmππ

δ

⎛ ⎞ ⎜ ⎟ ⎝ ⎠ : :N

if decoupled

Bose-Einstein Condensation

if identical bosonic particles are highly condensed in phase space and their total number is conserved and they thermalize then most of them go to the lowest energy available state

why do they do that?

by yielding their energy to the non-condensed particles, the total entropy is increased.

BEC preBEC

the axions thermalize and form a BEC after a time

t < � t > �

the axion fluid obeys classical field equations, behaves like CDM

the axion fluid does not obey classical field equations, does not behave like CDM

�

Quantum axion field dynamics

H =�

j

�ja†jaj +

�

ijkl

14�ijkla

†ka

†l aiaj

From self-interactions

From gravitational self-interactions

14!

�⇥4

� ⇥p3,⇥p4� ⇥p1,⇥p2 = �⇥

4m2V�⇥p1+⇥p2,⇥p3+⇥p4

� �p3,�p4g �p1,�p2 = �4⇥Gm2

V��p1+�p2,�p3+�p4

�1

|⇤p1 � ⇤p3|2+

1|⇤p1 � ⇤p4|2

⇥

O. Erken et al., PRD 85 (2012) 063520

After , axions thermalize in the “condensed” regime

implies

�

t1

� >> �E

d

dtNl = i

�

ijk

12(�klija

†ia

†jakal � h.c.)

� � 14n�m�2 for

and for self-gravity

�⇥4

(⇥ � 1/�p)� � 4�Gnm2⇥2

Thermalization occurs due to gravitational interactions

at time 1t

-1with v)l mδ= (

1 ( )( ) / ( ) ( )g a tt H t t a t −Γ ∝ ∝

2

2

Gmq

q

PS + Q. Yang, PRL 103 (2009) 111301

�g � 4�Gnm2l2

� 5 · 10�7H(t1)�

f

1012 GeV

⇥ 23

Gravitational interactions thermalize the axions and cause them to form a BEC when the photon temperature

After that 1vm t

δ

:

3 3( ) / ( ) ( )g t H t t a t−Γ ∝

T� � 500 eV�

f

1012 GeV

⇥ 12

Axion BEC thermalization has also been discussed by

•  Saikawa and Yamaguchi, Phys. Rev. D87 (2015) 085010

•  S. Davidson and Elmer, JCAP 1312 (2013) 034 •  J. Berges and J. Jaeckel, Phys. Rev. D91 (2015)

025020

•  A. Guth, M.P. Hertzberg and C. Prescod-Weinstein, Phys. Rev. D92 (2015) 103513

Guth et al. write: " ... we conclude that while a Bose-Einstein condensate is formed, the claim of long-range correlation is

unjustified."

the axion BEC is inhomogeneous because it is gravitationally unstable. However it does have the long range correlations that are characteristic of BEC. The BEC correlation length is not to be identified with the scale of homogeneity.

homogeneity length scale

BEC correlation length

Tidal torque theory

neighboring protogalaxy

Stromberg 1934; Hoyle 1947; Peebles 1969, 1971

Tidal torque theory with ordinary CDM

neighboring protogalaxy

the velocity field remains irrotational

v 0∇× =ur r

Tidal torque theory with axion BEC

v 0∇× ≠ur r

in their lowest energy available state, the axions fall in with net overall rotation

simulation by Arvind Natarajan

in case of net overall rotation

The caustic ring cross-section

an elliptic umbilic catastrophe

D -4

On the basis of the self-similar infall model (Filmore and Goldreich, Bertschinger) with angular momentum (Tkachev, Wang + PS), the caustic rings were predicted to be

in the galactic plane with radii

was expected for the Milky Way halo from the effect of angular momentum on the inner rotation curve.

( )1,2,3...n =

maxj 0.18≅

rot max40kpc v j220km/s 0.18

nn

a ⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

•  Axion Search Techniques

the cavity haloscope the axion helioscope

shining light through walls NMR methods axion mediated long-range forces

LC circuit atomic transitions

Axion dark matter is detectable

0Bur

γa

X

A/D FFT 0Bur001TME

ur

PS '83

La�� = g�a

fa�E · �B

3v 10c

β − = :

2 21

2)ah m c βν = (1 +

1aQ ν−

1LQ ν−

ν

dPdν

2 /am hc

610aQ :

Axion Dark Matter eXperiment see talks here by G. Carosi and B. Brubaker

Gen 2 ADMX sensitivity

Will scan the lower-mass decade at or below DFSZ sensitivity

Axion to photon conversion in a magnetic field

Theory

•  P. S. ’83 •  L. Maiani, R. Petronzio and E. Zavattini ’86 •  K. van Bibber et al. ’87 •  G. Raffelt and L. Stodolsky, ‘88 •  K. van Bibber et al. ’89

Experiment •  D. Lazarus et al. ’92 •  R. Cameron et al. ‘93 •  S. Moriyama et al. ’98, Y. Inoue et al. ’02 •  K. Zioutas et al. 04 •  E. Zavattini et al. 05

0Bur

γa

22

2 2sin

( )z

za

Lqg

af q

p γα

γπ 0

⎛ ⎞ ⎜ ⎟⎛ ⎞←→ = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎜ ⎟

⎝ ⎠

Β

x

with

conversion probability

2 2pl

2za

aE

mq

ω − =

Tokyo Axion Helioscope

CAST Collaboration: Phys. Rev. Lett. 112 (2013) 091302

Shining light through walls K. van Bibber et al. ‘87 A. Ringwald ‘03 R. Rabadan, A. Ringwald and C. Sigurdson ‘05 P. Pugnat et al. '05 C. Robilliard et al. '07 A. Afanasev et al. '08 A. Chou et al. '08 K. Ehret et al. '10

0Bur

γ

x 0Bur

γa

x

rate 41

af∝

Limits from "light through wall" axion searches

(a)

(b)

Wall Photon DetectoraγLaser

L

B0

Magnet

B0

Magnet

L

Matched Fabry-Perots

IOLaser

MagnetMagnet

Photon Detectors

Resonantly Enhanced Axion-Photon Regeneration

F. Hoogeveen (1996); P.S., D. Tanner and K. van Bibber (2007)

ALPS II at DESY

Expected sensitivity : 2 · 10�11 GeV�1

PVLASLaser experiments

Solar search

HB StarsResonantly enhancedphoton regeneration

ma (eV)10-6 10-5 10-4 10-3 10-2

10-16

10-8

10-10

10-12

10-14

10-4

10-6

g aγγ

(GeV

-1)

Microwave cavity dark matter searches

Axion models

Macroscopic forces mediated by axions

Theory:

J. Moody and F. Wilczek ’84 Experiment: A. Youdin et al. ’96 W.-T. Ni et al. ‘96

( )5ff ffa fa

mf

fL a i fg θγ + =

forces coupled to the f number density

forces coupled to the f spin density

1710fϑ− :background of magnetic forces

NMR with long range axion field

th

A. Arvanitaki and A. Geraci, 2014

⇥ = �NB0

the rotating mass on the left produces an oscillating axion field

the oscillating axion field is an effective magnetic field in an NMR experiment

Hint =gfmf�f

faa(x) Hint =

gfmffa

⇥�a(x) · ⇥�

de � 10�16 e cma(x)fa

the axion field induces an oscillating nuclear electric dipole moment

Axion dark matter detection using an LC circuit

to re

PS, D. Tanner and N. Sullivan, 2013

circuit should be cooled to milli-Kelvin temperatures

⇥⇤� ⇥Ba = ⇥ja ⇥ ga�� ⇥B0(⇥x) �ta(⇥x, t)

Axion dark matter detection using atomic transitions

- tune using the Zeeman effect - use laser techniques to count axion induced transitions - must cool to milli-Kelvin temperatures

PS 2014

Laf̄f = �gf2fa

⇥µa(x)f̄(x)�µ�5f(x)

f is electron, or nucleon

Haf̄f = +gf2fa

⇥�f · ⇥�aa

���

Conclusions

•  Axion dark matter is well motivated

•  Axion dark matter can be detected over most of the plausible mass range